interest per year. If the
interest is credited once (annually) at the end of the year, the
value of the account at year-
end will be $2.00. If the interest is credited twice in the year
(semi-annually), the interest rate
for each 6 months will be 50% (100%/2), so the initial $1 is
multiplied by 1.5 twice (1 to
include the original principal and .5 to add 50% more), yielding
$1.00×1.52 = $2.25 at the
end of the year. Compounding quarterly yields $1.00×1.254 =
$2.4414. This formula can be
written as:
- Imagine You Start With 1 00 In A Bank Account That Pays 100 Interest Per Year If The Interest Is Credited Once Annua 1 (1.28 KiB) Viewed 36 times
compounded per year.
1. Calculate the value of the $1 investment if the interest is
compounded
a. Monthly
b. Weekly
c. Daily
d. 1000 times in a year
2. Is there a big different between compounding monthly and 1000
times/year? Is this a
surprising result to you?
3. Use a graphing calculator or www.desmos.com/calculator , make
a graph of the investment
value results you calculated in part (1) and the data given in the
top paragraph. As a start,
look at a window such as -100<x<1200 and -1<y<4, where
x is representing the values for n.
Take a screen shot and include it.
4. What is the amount if interest is compounded hourly?
5. What is the amount if n=1,000,000,000?
6. Do you think the value of the $1 investment can grow
unbounded (to infinity)? What does
your graph suggest? Is there a limit of some sort? If so, what is
it?
SI: